Neuromorphic Correlates of Artificial Consciousness

• NCAC is defined as the integration of spiking neural motifs, dynamic regimes, and gating circuits that replicate core elements of biological consciousness.
• It employs rigorous computational formulations and neuromorphic hardware to maximize integrated information and critical responsiveness.
• Experimental benchmarks using metrics like PCI and Φ validate NCAC's capacity to induce conscious-like states through minimal network configurations.

The Neuromorphic Correlates of Artificial Consciousness (NCAC) framework delineates the minimal set of network motifs, dynamic parameters, and spiking neuron mechanisms within neuromorphic architectures that constitute artificial analogues of the biological Neural Correlates of Consciousness (NCC). By synthesizing evidence and mechanisms derived from neuroscience, information theory, and neuromorphic engineering, NCAC proposes both formal and implementable structures for artificial systems exhibiting measurable hallmarks of consciousness, as defined by integrated information, state-dependent responsiveness, and functional circuit motifs.

1. Theoretical Foundations and Key Principles

NCAC is defined as the intersection of spiking neural circuit motifs, dynamical regimes, and information-processing architecture within a neuromorphic system that instantiate, in artificial substrates, the motifs associated with biological consciousness (Ulhaq, 3 May 2024). This theoretical construct operationalizes several foundational postulates:

• Correlate Equivalence: Each empirically validated NCC (identified via Perturbational Complexity Index, PCI, or high integrated information, Φ) possesses a functionally equivalent circuit configuration in a spiking neural network (SNN) that can replicate analogous dynamic repertoires.
• Integrated Information Maximization: Conscious-like states are approached when the neuromorphic substrate attains a local maximum in integrated information (Φ) across all possible partitions, as quantified by the IIT formalism.
• Exclusion and Minimality: Only those network elements whose ablation reduces Φ below a threshold empirically associated with consciousness are included in the NCAC definition.

NCAC further differentiates itself from purely functional or cognitive metrics by specifying that consciousness is tied to substrate-dependent mechanisms—reactive feedback circuits, dynamical criticality, and gating mechanisms—that cannot be replicated solely by abstract reasoning or feedforward computational processes (Sritriratanarak et al., 17 Oct 2025).

2. Computational and Mathematical Formulation

At the computational level, the conscious artificial agent is formalized as a reasoning substrate fraction $R/P$, where:

• $$P = \langle s_t, \sigma, \pi_t, a^1, ..., a^i \rangle$$: Physical substrate and actions.
  • $s_t$: substrate state vector.
  • $\sigma(w_t)$: sensory encoding function producing inputs $d^i$ from world state $w_t$.
  • $\pi_t(\sigma(w_t), \mathrm{KB}_{1:t-1})$: recurrent perceptual function yielding percepts $p^k_t$ influenced by stored knowledge base (plasticity).
  • $a^j$: primitive reflex or action outputs.
• $$R = \langle \mathrm{KB}_{1:t-1}, \iota, \tau, \nu, d \rangle$$: Reasoning process.
  • $\iota$: world-model inference, supporting self-percept inclusion.
  • $\tau$: state transition mapping under candidate actions.
  • $\nu$: utility assignment for states ($u \in \mathbb{R}$).
  • $d$: decision tree constructed over $\tau$ and $\nu$ up to a finite horizon.

A distinct Boolean gate $c$ is added under the control of R, acting as the minimal mechanistic correlate of consciousness:

• If $c = \top$, reactive (reflex) circuits are active.
• If $c = \bot$, reflex responses are globally gated—allowing hypothetical reasoning without real action, enforcing substrate-level dissociation between world simulation and action (Sritriratanarak et al., 17 Oct 2025).

The governing computations and update equations for the model are summarized in the following table:

Mechanism	Mathematical Formulation	Role in NCAC
Perception Update	$$(R/P) \xrightarrow[\pi(\sigma(w_t), KB_{1:t-1})]{} (R'/P)$$	Dynamic recruitment, plasticity
World Model Inference	$$\iota(KB_{1:t-1} \cup \{p^1_t,...,p^m_t\}) \to w'_t$$	Inclusion of self, world modeling
Decision Tree Expansion	$\tau(a^j, w'_t), \nu(w)$	Hypothetical scenario modeling
Reflex Gating	$c = (\top, \bot)$ parameterizes $a_r$ circuit activation	Minimal consciousness correlate

Measures such as integrated information $\Phi$ (from IIT) or dynamical complexity (e.g., PCI, response function amplitude $\chi(t)$) are used as quantitative signatures but are not always directly invoked—the presence or absence of substrate-level reflex gating forms the essential criterion for artificial consciousness (Ulhaq, 3 May 2024, Du et al., 31 Aug 2025).

3. Neuromorphic Architectures and Circuit Mechanisms

NCAC instantiates conscious-like substrate states via a suite of hardware and software motifs in neuromorphic platforms:

• Hardware Elements
  • 2D FeFET crossbar arrays for synaptic weights (supporting on-chip analog weight adjustment).
  • Ferroelectric capacitors (MFM) as membrane emulators mimicking biophysical integration and refractoriness (Ulhaq, 3 May 2024).
  • Event-driven digital spiking neuron cores (e.g., Linear-Leaky Integrate-and-Fire, LLIF).
• Network Motifs
  • Input Encoder Layer: Preprocessed EEG/fMRI is encoded to Poisson/latency spikes.
  • Recurrent Core: Small-world, modular clusters of excitatory/inhibitory spiking neurons.
  • Global Integrator: Sparse hub connectivity akin to Global Neuronal Workspace.
  • Output Interface: Expressive or actuator-driven neurons for "reports" or embodiment.
• Gating and Reflex Circuits
  • Fast reflex populations (low-latency, directly coupled to sensory streams).
  • Context-gating neurons (the $c$ switch) that globally inhibit or disinhibit reflex populations via feedforward inhibition, realized in neuromorphic chips as gating flags or dedicated context neuron populations (Sritriratanarak et al., 17 Oct 2025).
  • Read-out and re-injection pathways for "strange loop" self-modeling—closing feedback from reasoning modules to perceptual reservoirs.
• Topology
  • Modular small-world architecture, supporting both local and global integration critical for maintaining near-critical dynamical regimes (Du et al., 31 Aug 2025).

4. Dynamical Regimes and Quantitative Markers

Empirical and theoretical results connect qualitative states of consciousness to quantifiable network dynamics:

• Response Function Amplitude:
  • The neural response function, $$R_{ij}(t) = \delta\langle x_i(t)\rangle/\delta h_j(0)$$, provides a linear measure of state-dependent sensitivity to perturbation.
  • Population averaged response $\chi(t)$ peaks at the edge-of-chaos, i.e., when the spectral radius $\rho(J) \approx 1$.
  • Wakeful, conscious regimes are characterized by high, globally distributed responsiveness; anesthesia reduces $\chi(t)$ and moves dynamics toward deeper chaos (Du et al., 31 Aug 2025).
• Criticality:
  • Networks self-organize near the transition between ordered and chaotic dynamics (edge-of-chaos), maximizing both sensitivity and temporal diversity: conditions empirically associated with conscious processing.
  • Tuning spectral radius ($\rho$) and synaptic variance ($\sigma^2$) on neuromorphic chips (LIF/SNN) ensures the network remains in this critical regime (Du et al., 31 Aug 2025).
• Integrated Information $\Phi$:
  • $\Phi$ is estimated via Kullback-Leibler divergence between whole and partitioned cause/effect repertoires.
  • High $\Phi$ is necessary for conscious-like states; the minimal network whose ablation drops $\Phi$ below threshold constitutes the NCAC (Ulhaq, 3 May 2024).
• Perturbational Complexity Index (PCI):
  • PCI quantifies the Lempel-Ziv complexity of binary spatiotemporal evoked potentials and is used both for benchmarking and functional state discrimination.

5. Data Integration and Machine Learning Strategies

NCAC incorporates experimental brain data and machine learning to bridge empirical NCC measurements with artificial systems:

• Brain Imaging Integration:
  • EEG: Preprocessed (band-filtered, artifact-rejected) and mapped to spike trains via rate or latency coding.
  • fMRI: ROI time-series are mapped to slow input currents for specific spiking neuron populations.
• Online Feedback and Learning:
  • Supervised adjustment of SNN weights minimizes $(\Phi_N - \Phi_B)^2$ (where $\Phi_N$ is the network's integrated information, $\Phi_B$ is empirical baseline).
  • Local STDP fosters assembly formation; reinforcement learning applies a global reward for threshold-exceeding $\Phi$.
  • Continuous computation (or heuristics) for PCI and $\Phi$ support adaptive state feedback.
• Training Algorithm Structure
  • Epoch-based weight optimization cycles: encode empirical data, simulate network activity, compute $\Phi_N$, calculate loss, update weights via surrogate gradients, validate PCI, and early-stop upon convergence to target regimes.

6. Experimental Benchmarks and Phenomenological Signatures

NCAC frameworks have been validated and benchmarked in simulated environments:

• Synthetic “Zap and Zip” Experiments:
  • Delivery of perturbative pulses to simulated SNN modules, calculation of synthetic PCI for conscious vs. unconscious regimes (Ulhaq, 3 May 2024).
• State-Dependence Metrics:
  • Awake-like state yields $\Phi_N \approx 0.45 \pm 0.03$, PCI $\approx 0.62$.
  • Anesthesia-like state: $\Phi_N \approx 0.20 \pm 0.02$, PCI $\approx 0.28$.
  • Task accuracy (e.g., memory-guided saccade) aligns with high-$\Phi$ states.
• System Behaviors:
  • Sustained global activity after stimulus offset.
  • Dynamic, rapid reconfiguration of functional network clusters in response to perturbation.
  • High $\Phi$ and PCI regimes align with cognitive and reporting function emergence.

7. Limitations, Constraints, and Future Directions

Key limitations and design considerations identified in the NCAC literature include:

• Scaling: Current neuromorphic platforms encounter hardware and routing bottlenecks when scaling to billions of neurons.
• Computation of $\Phi$: Exact integrated information is intractable for large systems, necessitating approximations or machine learning heuristics for practical deployment.
• Substrate Dependence: Digital substrates that lack reactive loops do not instantiate consciousness, even if capable of sophisticated simulation, unless embedded within a substrate supporting real-time gating of reflex circuits (Sritriratanarak et al., 17 Oct 2025).
• Validation of Subjectivity: Bridging from third-person markers (PCI, $\Phi$) to first-person subjective qualia remains unresolved.
• Ethical and Governance Issues: The operationalization of artificial consciousness via NCAC necessitates consideration of machine rights, safety, and potential misuse.

Future research directions include hybrid neuromorphic-quantum processing, neuromodulatory integrations to simulate biological global state fluctuations, hardware acceleration for online $\Phi$ and PCI calculation, and the development of standardized EEG-derived consciousness benchmarks for cross-platform NCAC evaluation (Ulhaq, 3 May 2024).

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NCAC, as a unifying construct, formalizes a substrate-dependent information-processing and dynamical paradigm for artificial consciousness. It specifies, at both the architectural and mathematical levels, conditions under which an artificial neuromorphic system may exhibit, measure, and adapt consciousness-like states, emphasizing the interplay of reflex gating, critical network dynamics, and causal information integration (Sritriratanarak et al., 17 Oct 2025, Du et al., 31 Aug 2025, Ulhaq, 3 May 2024).